Discussion
Consider the LP problem :
Max \(Z = 10x_{1} + 6x_{2}\)
Subject to the constraints :
\(5x_{1} + 3x_{2} \le 30;\)
\(x_{1} + 2x_{2} \le 18\) and
\(x_{1}, x_{2} \ge 0.\)
Then the LP has :
Answer: B
The LP has multiple feasible solutions.
The origin satisfies both constraints, so the feasible region is non-empty, and it is a polygon with vertices (0, 0), (6, 0), (6/7, 60/7) and (0, 9). Any non-empty polygon of positive area contains infinitely many feasible points.
In fact the objective \(10x_{1} + 6x_{2} = 2(5x_{1} + 3x_{2})\) is parallel to the first constraint, so even the optimum (Z = 60) is reached along the whole edge from (6, 0) to (6/7, 60/7). The problem certainly has feasible solutions, more than one of them, and enough is known to say so.
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development